Leaf languages and string compression

Abstract

Tight connections between leafs languages and strings compressed
via straight-line programs (SLPs) are established. It is shown
that the compressed membership problem for a language $L$ is complete
for the leaf language class defined by $L$ via logspace machines.
A more difficult variant of the compressed membership problem for
$L$ is shown to be complete for the leaf language class defined
by $L$ via polynomial time machines. As a corollary,
a fixed linear visibly pushdown language with
a PSPACE-complete compressed membership problem is obtained.
For XML languages,
the compressed membership problem is shown to be coNP-complete.